Step 1: Separate the combined inequality into two individual inequalities. The given inequality is $$-1 \le \frac{5-2x}{3} < 2x-1$$ This can be split into two inequalities: 1) $$-1 \le \frac{5-2x}{3}$$ 2) $$\frac{5-2x}{3} < 2x-1$$ Step 2: Solve the first inequality. $$-1 \le \frac{5-2x}{3}$$ Multiply both sides by 3: $$-1 \times 3 \le 5-2x$$ $$-3 \le 5-2x$$ Subtract 5 from both sides: $$-3 - 5 \le -2x$$ $$-8 \le -2x$$ Divide both sides by -2. Remember to reverse the inequality sign when dividing by a negative number: $$\frac{-8}{-2} \ge x$$ $$4 \ge x$$ So, $x \le 4$. Step 3: Solve the second inequality. $$\frac{5-2x}{3} < 2x-1$$ Multiply both sides by 3: $$5-2x < 3(2x-1)$$ $$5-2x < 6x-3$$ Add $2x$ to both sides: $$5 < 6x + 2x - 3$$ $$5 < 8x - 3$$ Add 3 to both sides: $$5 + 3 < 8x$$ $$8 < 8x$$ Divide both sides by 8: $$\frac{8}{8} < x$$ $$1 < x$$ So, $x > 1$. Step 4: Combine the solutions from both inequalities. From Step 2, we have $x \le 4$. From Step 3, we have $x > 1$. Combining these two, we get the combined inequality: $$1 < x \le 4$$ The final answer is $\boxed{1 < x \le 4}$. Send me the next one 📸